The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  2  0  2  1  1  1  1  X  1  1  1  1  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0  X X+2  X  X  0  X  0  2 X+2  0 X+2  0 X+2  0  2  0
 0  0  X  X  0 X+2  X  0  0  X  X  2 X+2  X  0 X+2  X  X  X  2  X  X  X  0  X  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  0  2  2  2  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  2  2  0  2  0  2  2  0  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  0  2  0  2  0  2  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  0  2  2  2  0  0  0  2  0  2  0  2  2  0

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+186x^22+433x^24+64x^25+869x^26+512x^27+1487x^28+896x^29+1585x^30+512x^31+925x^32+64x^33+394x^34+158x^36+36x^38+17x^40+1x^42+3x^44+1x^46

The gray image is a code over GF(2) with n=116, k=13 and d=40.
This code was found by Heurico 1.16 in 1.59 seconds.